A similar thing happened with my boyfriend. He got extremely drunk one night and kissed another girl, a lot. It was about 6 months into our relationship and it actually took that happening for me to realise just how much I cared about it. He didn't get her number though, it was just....I'm not sure how to explain it. There was never any chance of him contacting her again, and if he'd tried I definitely would have told him where to stick it.
It made things between us difficult, what hurt more than anything was that he'd broken my trust for nothing (it wasn't as though he was cheating on me because he wanted us to be over or because he wanted to be with her). If you want to move on from it it won't be easy. To be honest I think the least she could do if she wants you to forgive her is to get rid of his contact details.
My boyfriend worked so hard to regain my trust, he explained everything to me, gave me time to think, let me shout and scream at him or cry on his shoulder, and has done a lot to regain my trust. I still feel sick thinking about them together, but we've been together for 2 and a half years now. I'm not gonna give you crap about how it's made our relationship stronger, because it's given us a lot of stress. But I felt that it was worth saving. Forgiving was the easy part, it was the forgetting that was hardest for me. If he'd have slept with her I couldn't have coped but thankfully he didn't cross that line.
Time away from her will probably be good for you both, and allow you to think about whether she's really worth carrying on the relationship.